- #1
Trying2Learn
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- TL;DR Summary
- I cannot extract the Euler-Lagrange equation with different variation functions
Good Morning all
Yesterday, as I was trying to formulate my confusion properly, I had a series of posts as I circled around the issue.
I can now state it clearly: something is wrong :-) and I am so confused :-(
Here is the issue:
I formulate the Lagrangian for a simple mechanical system (let's go with 1D)
I formulate the variation of the position and the variation of the velocity, use the Gateaux derivative, work it though..
However, as I understand, I MUST vary the position and velocity INDEPENDENTLY!
And that is where the problem begins (for me)
Could someone read the attached, one page and tell me where I go wrong?
(And if someone can tell me how, I can post a Matlab code that actually tries DIFFERENT eta functions and shows that the correct solutoin produces a stationary Action -- and plots the area between KE and PE)
Yesterday, as I was trying to formulate my confusion properly, I had a series of posts as I circled around the issue.
I can now state it clearly: something is wrong :-) and I am so confused :-(
Here is the issue:
I formulate the Lagrangian for a simple mechanical system (let's go with 1D)
I formulate the variation of the position and the variation of the velocity, use the Gateaux derivative, work it though..
However, as I understand, I MUST vary the position and velocity INDEPENDENTLY!
And that is where the problem begins (for me)
Could someone read the attached, one page and tell me where I go wrong?
(And if someone can tell me how, I can post a Matlab code that actually tries DIFFERENT eta functions and shows that the correct solutoin produces a stationary Action -- and plots the area between KE and PE)
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